Moments of claims in a Markovian environment

Bara Kim; Hwa Sung Kim

doi:10.1016/j.insmatheco.2006.07.004

Moments of claims in a Markovian environment

Bara Kim, Hwa Sung Kim

Department of Mathematics

Research output: Contribution to journal › Article

17 Citations (Scopus)

Abstract

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.

Original language	English
Pages (from-to)	485-497
Number of pages	13
Journal	Insurance: Mathematics and Economics
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/j.insmatheco.2006.07.004
Publication status	Published - 2007 May 1

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Keywords

Circumstance process
Discounted aggregate claims
Laplace-Stieltjes transform
Moments

ASJC Scopus subject areas

Statistics, Probability and Uncertainty
Economics and Econometrics

Cite this

Kim, B., & Kim, H. S. (2007). Moments of claims in a Markovian environment. Insurance: Mathematics and Economics, 40(3), 485-497. https://doi.org/10.1016/j.insmatheco.2006.07.004

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Access to Document

10.1016/j.insmatheco.2006.07.004